The invention is based on an apparatus as defined hereinafter. An apparatus is already known in which a second carrier, having a second resistor layer, is disposed downstream of a first carrier having a measuring resistor layer in a parallel section of a flow cross section. As a result, although deposits of dirt which cause a change in the characteristic curve of the measuring resistor layer are prevented from forming on the face of the first carrier, which points upstream and has the measuring resistor layer, nevertheless such an arrangement has the disadvantage that upon slight changes in the position of the second carrier, the flow around the first carrier is changed quite severely, and so the measurement signal of the measuring resistor layer is undesirably changed severely as well.